Neighborhoods of points in codimension-one submanifolds lie in codimension-one spheres
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- by Fredric D. Ancel PDF
- Proc. Amer. Math. Soc. 103 (1988), 1315-1316 Request permission
Abstract:
For $n \geq 4$, let $M$ be an $(n - 1)$-manifold embedded in an $n$-manifold $N$. For each point $p$ of $M$, there is an $(n - 1)$-sphere $\Sigma$ in $N$ such that $\Sigma \cap M$ is a neighborhood of $p$ in $M$.References
- Fredric D. Ancel, Resolving wild embeddings of codimension-one manifolds in manifolds of dimensions greater than $3$, Topology Appl. 24 (1986), no. 1-3, 13–40. Special volume in honor of R. H. Bing (1914–1986). MR 872476, DOI 10.1016/0166-8641(86)90047-7
- R. H. Bing, A surface is tame if its complement is $1$-ULC, Trans. Amer. Math. Soc. 101 (1961), 294–305. MR 131265, DOI 10.1090/S0002-9947-1961-0131265-1
- Robert J. Daverman, Embeddings of $(n-1)$-spheres in Euclidean $n$-space, Bull. Amer. Math. Soc. 84 (1978), no. 3, 377–405. MR 645404, DOI 10.1090/S0002-9904-1978-14476-0
- Robion C. Kirby, On the set of non-locally flat points of a submanifold of codimension one, Ann. of Math. (2) 88 (1968), 281–290. MR 236900, DOI 10.2307/1970575
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 1315-1316
- MSC: Primary 57N35
- DOI: https://doi.org/10.1090/S0002-9939-1988-0955028-4
- MathSciNet review: 955028